Sound Experiments on Superfluidity of 3He in Highly Porous Aerogels

We have carried out sound experiments on superfluid ³ He in three highly porous aerogels with different porosities. Two of the acoustic cells contain aerogels inside the pores in roughly sintered silver powder to avoid the vibration of the aerogel. In these acoustic cells we have detected fourth sound, and extracted the superfluid density from the fourth sound velocity. The effect of the sintered silver on superfluid ³ He was examined by using another acoustic cell which contains the sintered silver without aerogel. The size of the pores in the sintered silver was large enough not to show the size effect of superfluid ³ He and small enough to observe fourth sound of ³ He. In another cell without sintered silver, we have observed second-sound-like signal. The superfluid transition temperatures of ³ He are suppressed more in higher density aerogel. The aerogel density dependence of the suppression of the superfluid transition temperature of ³ He in aerogel can be explained qualitatively by the simple s-wave scattering approximation. However, the superfluid density shows quite different pressure-dependence in different porous aerogels. The reason of this phenomenon is not understood yet.     

Fourth Sound Measurement of Superfluid 3He in Aerogel

The fourth sound resonance experiment has been done on liquid ³He in 98.5% porosity aerogel. Aerogel was grown inside the pores among the sintered silver powder to avoid the vibration of the aerogel strands by the sound experiment. The measurement was performed at zero magnetic field and 27 bar. We observed the phase transition between the A-like and B-like phases and also their coexistent state. The A-like to B-like phase transition occurs not at a temperature but within a temperature band. In this band, the A-like phase gradually converts to the B-like phase. Possible picture of the coexistent state is discussed.     

Acoustic Resonance of Superfluid 3He in Parallel Plates

We performed an acoustic resonance experiment of superfluid ³He confined in a stack of parallel plates, and found the fourth sound resonance. From its velocity, the superfluid density fraction was calculated. No size effect was found because the gap between parallel plates were much larger than the superfluid coherence length. The energy loss of the resonance was also measured. We found that the hydrodynamic theory qualitatively described its temperature dependence, but it could not describe the gap width dependence. Possible explanations is discussed in the text. More over, we found the unidentified resonance that cannot be explained by conventional sound modes.     

Physical Mechanisms for Effective Mass Enhancement in 3He

We use structural information from simulations and from variational ground state calculations for calculating the effective mass of ³He at zero temperature. It is found that the relatively large effective mass is due to a combination of several physical effects: Density fluctuations cause an effective mass enhancement due to predominantly hydrodynamic backflow. This effect is, around the Fermi momentum, a smooth function of the single particle wave number; its magnitude is consistent with the effective mass of ⁴He impurities in ³He. Spin-fluctuations, on the other hand, cause a pronounced peak of the effective mass around the Fermi wave number. We also find, consistent with earlier work, an instability of the single particle spectrum at about 2.5 k _F, this is due to the coupling to density fluctuations in the maxon region.     

Turbulence of Second Sound Waves in Superfluid 4He: Effect of Low-Frequency Resonant Perturbations

We report the results of investigations of acoustic turbulence in a system of nonlinear second sound waves in a high-quality resonator filled with superfluid ⁴He. It was observed that subharmonics of a periodic driving force applied to the system may be generated via a parametric instability. We find that application of an additional low-frequency pumping to the turbulent system results in the generation of waves at combination frequencies of the driving forces and also leads to substantial changes in the energy spectrum of the acoustic oscillations.      

Acoustic Spectroscopy of Superfluid 3He in Aerogel in the Presence of a Magnetic Field

We have constructed a silver alloy cell to investigate low frequency sound propagation in ³ He-filled aerogel at various magnetic fields. In this apparatus, two sound modes were observed in the superfluid phase. We observed both the first sound-like mode (fast mode) which is a compression wave also seen in the normal state and the second sound-like mode (slow mode) which is attributed to the out-of-phase oscillation of the superfluid and normal components of ³ He clamped to the aerogel matrix. The values of T_c and _s can be extracted from the analysis of these two modes. In addition, a Helmholtz resonance provides an in-situ signature of the bulk superfluid transition and allows us to also determine the bulk _s. By measuring these quantities over a range of applied magnetic fields we hope to explore the P, T, H phase diagram of ³ He in aerogel.     

Quantum Fluid Dynamics of Rotating Superfluid 3He in Aerogel

Superfluid ³He A-like and B-like phases in 98% aerogel have been studied under rotation up to 2π rad/s by using cw-NMR and Homogeneous Pressing Domain (HPD) NMR at 29 mT and 3.0 MPa. Triplet superfluid ³He has continuous symmetries whose degeneracies are lifted by small perturbations of magnetic field, boundary condition of the sample cell, counterflow and global anisotropies of aerogel. We report NMR results of the two typical samples in aerogel under rotation, which are almost identical in the phase diagram, T _c and the critical velocity of the multiplication of vortex but are very different in textures and responses to the flow with each other. One samples (S-D) is slightly compressed by squeezing and thermal stress and thus has global anisotropic deformation along the sample axis. The other cell (S-H) has randomly(not uniaxially)-oriented global anisotropy. In the S-D, we observed a large negative shift in cw-NMR and spin wave and HPD in the B-like phase. Comparing textures determined by NMR and its response to the counterflows between two samples, we discuss how the long-range order of the continuous symmetry and textures are controlled by orientation effects due to global anisotropy in aerogel.      

A high capacity completely closed-cycle 250 mK He refrigeration system based on a pulse tube cooler

We present the design of a completely closed-cycle refrigeration system. The system consists of four stages; the first two, 40.5 and 2.7 K, are provided by a pulse tube cooler, the third and fourth stages by helium adsorption refrigerators. The adsorption refrigerators use ⁴He and ³He with base temperatures of 700 and 250 mK, respectively. Performance tests including some with the cooler rotated from the vertical showed that with a load of 15 μK, a temperature below 286 mK can be maintained for 72 h.     

Superfluid Phase Transition of 3He-4He Mixture Films Adsorbed on Alumina Powder

The superfluid phase transition of ³ He- ⁴ He mixture films adsorbed on 500 Å alumina powder has been studied for mixture films whose superfluid thickness is less than a monolayer. The transitions are found to be controlled by the Kosterlitz-Thouless critical line, but a strong broadening of the transition is observed as the ³ He concentration is increased. Analyzing the broadening in terms of a KT vortex-pair theory modified for the the finite powder size yields a vortex core parameter which increases nearly linearly with added ³ He. Also observed in these measurements is a temperature-dependent and ³ He-dependent depletion of the superfluid density at low temperatures, which is thought to arise from the high-frequency ripplon/third sound excitations of the film.     

Temperature and Concentration Relaxation in Phase-separated Superfluid 3He–4He Mixtures

The kinetics of the temperature and concentration variations in the superfluid ³He–⁴He mixtures with initial concentration of 9.8% ³He, and heated from below, was studied experimentally under the pressure of 0.38 bar over a temperature range of 150–400 mK. It is found that in contrast to homogeneous liquids, the temperature and concentration relaxation in phase-separated mixtures can be described by a superposition of two exponential processes in which the time constants of temperature and concentration variations coincide. If the initial mixture was homogeneous and phase separation was triggered by a heat flow, the temperature and concentration vary non-monotonically and exhibit anomalous features at the moment of phase separation. In this case the phase transition starts in the metastable superfluid, formed out of a quite supersaturated mixture where the nucleation of the new phase may be caused by quantized vortices. The results are analyzed in terms of two possible mechanisms of relaxation–the acoustic mechanism with the second sound velocity and the diffusive one connected with dissipative flows of impurity and thermal excitations. It is shown that the measured relaxation times agree with a prediction of the theory.      

A-B Phase Conversion and Coexistence of Superfluid 3He in Aerogel

We have studied phase transition of superfluid ³He at 2.4 MPa in cylindrical aerogel by NMR method. When the liquid is cooled down from the normal state, the A-like phase appears below superfluid transition temperature T _c ^a which is suppressed in comparison with the transition temperature of the bulk liquid. With further cooling below the certain temperature T _ab,c ^a , the A-like phase is converted into the B-like phase gradually. Both phases stably coexist within about 90 μK. When you keep the temperature constant in which both phases coexist, the A-B phase conversion stops. With furthermore cooling, the whole liquid becomes the B-like phase. The cwNMR spectra at the coexistence state suggest that the B-like phase is not uniformly distributed in the A-like phase like a large number of small bubbles in a liquid, but separated as a whole from the A-like phase. By applying a field gradient which changes as a function of square of radius, we found that the A-like phase is in the edge part with a cylindrical shape and the B-like phase is in the central part with a columnar shape.      

Vibrating Wire Measurements in 3He-4He Mixtures in the Ballistic Quasiparticle Regime

We present our first high resolution vibrating wire resonator data on dilute ³ He- ⁴ He mixtures at ultra low temperatures. Measurements were performed at saturated vapor pressure with ³ He concentrations below the phase separation limit. The behavior of the damping at very low temperatures does not follow the modified slip correction analysis previously applied to extend the validity of the hydrodynamic treatment.     

The Formation and Melting of 3He Clusters in Phase-Separated Solid 3He-4He Mixtures

Melting pressure measurements have been made on the ³ He-rich phase formed by cooling a solid mixture of 0.6% ³ He in ⁴ He through phase separation, at pressures between 2.78 and 3.56 MPa. For comparison, simultaneous observations were made with the mixture confined in the pores of a silver sinter and in an open volume connected to the same fill-line. Samples in the sinter cell solidify at higher pressures than the open cell and equilibrate more quickly. Both cells exhibit hysteresis between melting and freezing temperatures, and the transitions are broader in the open-volume cell. Relative to pure ³ He, the melting pressure is elevated by as much as 60 kPa in the sinter cell and 20 kPa in the open cell. The size of the pressure change on melting indicates that a large fraction of the ³ He remains solid at pressures below the melting curve, and this effect is more pronounced in the sinter cell. Measurements are in progress to measure the magnetisation through the magnetic ordering transition.     

Magnetic Distortion of the B-like Phase of Superfluid 3He Confined in Aerogel

We present measurements of the response of the B-like phase of superfluid ³He in aerogel to an applied flow. The measurements are made using a cylindrical piece of 98% silica aerogel attached to a vibrating wire resonator. The resonator is immersed in superfluid ³He at 16 bar pressure and at low temperatures. A variable magnetic field is applied such that the aerogel-confined superfluid may exist in the A-like or B-like phase, while the surrounding fluid is always in the bulk B-phase. The resonator response reveals a velocity dependence of the inferred aerogel-confined superfluid fraction. We discuss measurements of the temperature and magnetic field dependence of the response in the B-like phase. We find a significant field dependence indicating a strong magnetic distortion of the B-like phase order parameter.      

3He Impurities in 4He Systems Adsorbed on Curved Substrates

It is shown that ³He impurities in sufficiently large ⁴He systems adsorbed onto substrates with curved geometries form surface bound states, analogous to the Andreev state on a planar liquid--vapor interface. We report the analysis performed for superfluid ⁴He adsorbed on the external surface of the nano-fullerene C₆₀ and on cylindrical nano-wires of Au. It is found that a single ³He impurity diluted into such adsorbed structures behaves as on films on planar substrates and as on pure ⁴He clusters.     

Neutron experiments on solid3He in high field at very low temperature

The magnetic transition from the paramagnetic phase to the magnetically ordered high-field phase of solid³He is observed by polarized neutron transmission experiments. The transition shows the feasibility of neutron diffraction experiments on the high-field ground state of solid³He. The behavior of the boundary resistance between solid³He and silver powder in a magnetic field is discussed.     

Doppler shift in third and fourth sound in 3He-4He mixtures

The Doppler-shifted velocity of third sound in a system where the superfluid flows with velocity v _s is given. The calculations are to first order in v _s/u₃ where u ₃ is the third-sound velocity in the rest frame. We take into account the effects of the pressure and ³He concentration gradients normal to the substrate. Corresponding calculations for fourth sound are also given.Supported in part by the GFK, West Germany, through the Israel National Council for Research and Development.     

A continuous He cryostat with pulse-tube pre-cooling and optical access

We have designed and constructed a continuously operating ³He cryostat with windows for laser ablation and spectroscopy. A two-stage pulse-tube refrigerator cools two platforms to base temperatures of approximately 40 K and 4 K respectively. The platforms are equipped with heat exchangers that cool separate streams of ⁴He and ³He. The ⁴He stream is used to run a thermally isolated evaporative refrigerator with a base temperature of approximately 1.5 K and a cooling power of 20 mW. The ⁴He refrigerator is used to condense ³He, which is used to run a ³He evaporative refrigerator on the experimental cell. The cryostat runs continuously at temperatures from 10 K to 0.4 K with a cooling power of 1.5 mW at 0.5 K.     

Anisotropy of Superfluid 3He Near Free Surface Investigated by Surface State Electrons

We have measured the resistivity of a Wigner solid formed on the free surface of superfluid ³He in the A and B phases under magnetic fields. The mobility of the Wigner solid is limited by the collisions of thermally excited quasiparticles in ³He, and hence is very sensitive to the distribution of quasiparticles in momentum space. The observed resistivity of the Wigner solid in the A phase asymptotically approaches the temperature-square dependence at low temperatures, reflecting the A phase gap with point nodes. Its temperature dependence is well explained by the vector being uniformly aligned normal to the surface. The resistivity in the B phase, in contrast, exhibits an exponential decrease at low temperatures. The resistivity in the small field well agrees with the behavior expected for the isotropic gap in the BW state. The resistivity increases in high magnetic fields, which is explained by the combination of the distortion of the gap in the BW state by the field and the orientation of the order parameter caused by the free surface.      

Compressing Spin-Polarized 3He With a Modified Diaphragm Pump

Nuclear spin-polarized ³He gas at pressures on the order of 100 kPa (1 bar) are required for several applications, such as neutron spin filters and magnetic resonance imaging. The metastability-exchange optical pumping (MEOP) method for polarizing ³He gas can rapidly produce highly polarized gas, but the best results are obtained at much lower pressure (~0.1 kPa). We describe a compact compression apparatus for polarized gas that is based on a modified commercial diaphragm pump. The gas is polarized by MEOP at a typical pressure of 0.25 kPa (2.5 mbar), and compressed into a storage cell at a typical pressure of 100 kPa. In the storage cell, we have obtained 20 % to 35 % ³He polarization using pure ³He gas and 35 % to 50 % ³He polarization using ³He-⁴He mixtures. By maintaining the storage cell at liquid nitrogen temperature during compression, the density has been increased by a factor of four.